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Niners (Posted on 2002-10-23) Difficulty: 4 of 5
The set of numbers {9, 99, 999, 9999, ...} has some interesting properties. One of these has to do with factorization. Take any number n that isn't divisible by 2 or by 5. You will be able to find at least one number in the set that is divisible by n. Furthermore, you won't need to look beyond the first n numbers in the set.

Prove it.

(from http://www.ocf.berkeley.edu/~wwu/riddles/)

See The Solution Submitted by levik    
Rating: 4.2500 (8 votes)

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Need some math theory help over here | Comment 11 of 15 |
I never studied math theory, but looking at this problem, it seems that for any n not divisible by 2 or 5, a string of n-1 9s should always be divisible by n. In other words, [10^(n-1)-1]modulo(n)=0. Can one of you theory whizzes prove/disprove this? (or is this some famous theorem of Euler et al?)
  Posted by Bryan on 2003-03-05 10:37:34
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